More than a thousand people took part in several events across Australia to mark the day, with Prime Minister Tony Abott appreciating Yoga's universal appeal.
"For thousands of years, yoga has provided its followers with a guide to bringing their mind, body and spirit into balance," Abott said.
"Yoga's universal and growing popularity demonstrates its appeal to people from all the walks of life and its great potential to foster better health among individuals and populations around the world," he said.
Several MPs including Victoria's speaker Telmo Languiller, Inga Peulich, Anthony Byrne attended the ceremony by lighting the lamp in the presence of Indian consul-general in Melbourne Manika Jain.
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Yoga events were also held at Sydney's popular Bondi beach and in the Australian capital Canberra.
In the UK, hundreds gathered across cities to celebrate the day with the main event on the bank of the river Thames in London. It was held at Bernie-Spain Garden, on the South Bank of Thames.
In China, events were organised at the prestigious Peking University and Geely University. People from different walks of life took part in the exercise.
About a week ahead of the International Yoga Day, the India-China Yoga college was inaugurated at Yunnan Minzu University in Kunming, the first such college in the country.